for all \(s \in \lbrace 2,3,\dots ,N_s\rbrace \) , with \(G_{1,k} = w_{1,k}\) . We are able to write the optimization problem in (REF ) as nested optimization subproblems due to the Markovian structure of the model in (REF )-(REF ). The approach of solving an optimization problem by recursively solving optimization subproblems is known as dynamic programming [1]}. There are two important things to note here. First, all optimization subproblems in (REF ), (REF ), and (REF ) are small-scale problems, depending only on a few optimization variables. Therefore, the operative memory required to compute the solution is much lower than for large-scale problem in (REF ). Second, for each \(s \in \lbrace 1,2,\dots ,N_s\rbrace \) , the solution \(w_{s,k}\)  in (REF ) can be computed independently and, thus, in parallel. Given sufficient computational power, parallelization greatly reduces the time required to solve the optimization problem. This makes it viable to use much longer measurement series for the identification of the system, which may considerably improve the accuracy of the identified model.
